Building a bridge between coordination compounds and clusters: bonding analysis of the icosahedral molecules [M(ER)12] (M = Cr, Mo, W; E = Zn, Cd, Hg)

The bonding situation of the icosahedral compounds [M(EH)(12)] (M = Cr, Mo, W; E = Zn, Cd, Hg), which are model systems for the isolated species [Mo(ZnCp*)(3)(ZnMe)(9)] possessing the coordination number 12 at the central atom M, have been analyzed with a variety of charge and energy decomposition methods (AIM, EDA-NOCV, WBI, MO). The results give a coherent picture of the electronic structure and the nature of the interatomic interactions. The compounds [M(EH)(12)] are transition metal complexes that possess 12 M-EH radial bond paths (AIM) that can be described as 6 three-center two-electron bonds (MO). The radial M-EH bonds come from the electron sharing interactions mainly between the singly occupied valence s and d AOs of the central atom M and the singly occupied EH valence orbitals (MO, EDA-NOCV). The orbital interactions provide ~42% of the total attraction, while the electrostatic attraction contributes ~58% to the metal-ligand bonding (EDA-NOCV). There is a weak peripheral E-E bonding in [M(EH)(12)] that explains the unusually high coordination number (MO). The peripheral bonding leads for some compounds [M(EH)(12)] to the emergence of E-E bond paths, while in others it does not (AIM). The relative strength of the radial and peripheral bonding in [Al(13)](-) and [Pt@Pb(12)](2-) is clearly different from the situation in [M(EH)(12)], which supports the assignments of the former species as cluster compounds or inclusion compounds (MO, WBI). The bonding situation in [WAu(12)] is similar to that in [M(EH)(12)].     

Oxidative properties of FeO2+: electronic structure and solvation effects

An electronic structure analysis is provided of the action of solvated FeO(2+), [FeO(H(2)O)(5)](2+), as a hydroxylation catalyst. It is emphasized that the oxo end of FeO(2+) does not form hydrogen bonds (as electron donor and H-bond acceptor) with H-bond donors nor with aliphatic C-H bonds, but it activates C-H bonds as an electron acceptor. It is extremely electrophilic, to the extent that it can activate even such poor electron donors as aliphatic C-H bonds, the C-H bond orbital acting as electron donor in a charge transfer type of interaction. Lower lying O-H bonding orbitals are less easily activated. The primary electron accepting orbital in a water environment is the 3sigma*alpha orbital, an antibonding combination of Fe-3d(z(2)) and O-2p(z), which is very low-lying relative to the pi*alpha compared with, for example, the sigma* orbital in O(2) relative to its pi*. This is ascribed to relatively small Fe-3d(z(2)) with O-2p(z) overlap, due to the nodal structure of the 3d(z(2)).The H-abstraction barrier is very low in the gas phase, but it is considerably enhanced in water solvent. This is shown to be due to strong screening effects of the dielectric medium, leading to relative destabilization of the levels of the charged [FeO(H(2)O)(5)](2+) species compared to those of the neutral substrate molecules, making it a less effective electron acceptor. The solvent directly affects the orbital interactions responsible for the catalytic reaction.     

Integration of electron density and molecular orbital techniques to reveal questionable bonds: the test case of the direct Fe-Fe bond in Fe2(CO)9

The article illustrates the advantages of partitioning the total electron density rho(rb), its Laplacian (inverted Delta)2 rho(rb), and the energy density H(rb) in terms of orbital components. By calculating the contributions of the mathematically constructed molecular orbitals to the measurable electron density, it is possible to quantify the bonding or antibonding character of each MO. This strategy is exploited to review the controversial existence of direct Fe-Fe bonding in the triply bridged Fe2(CO)9 system. Although the bond is predicted by electron counting rules, the interaction between the two pseudo-octahedral metal centers can be repulsive because of their fully occupied t(2g) sets. Moreover, previous atoms in molecules (AIM) studies failed to show a Fe-Fe bond critical point (bcp). The present electron density orbital partitioning (EDOP) analysis shows that one sigma bonding combination of the t(2g) levels is not totally overcome by the corresponding sigma* MO, which is partially delocalized over the bridging carbonyls. This suggests the existence of some, albeit weak, direct Fe-Fe bonding.     

Molecular orbitals of the oxocarbons (CO)n, n = 2-6. Why does (CO)4 have a triplet ground state?

Cyclobutane-1,2,3,4-tetrone has been both predicted and found to have a triplet ground state, in which a b(2g) σ MO and an a(2u) π MO are each singly occupied. The nearly identical energies of these two orbitals of (CO)(4) can be attributed to the fact that both of these MOs are formed from a bonding combination of C-O π* orbitals in four CO molecules. The intrinsically stronger bonding between neighboring carbons in the b(2g) σ MO compared to the a(2u) π MO is balanced by the fact that the non-nearest-neighbor, C-C interactions in (CO)(4) are antibonding in b(2g), but bonding in a(2u). Crossing between an antibonding, b(1g) combination of carbon lone-pair orbitals in four CO molecules and the b(2g) and a(2u) bonding combinations of π* MOs is responsible for the occupation of the b(2g) and a(2u) MOs in (CO)(4). A similar orbital crossing occurs on going from two CO molecules to (CO)(2), and this crossing is responsible for the triplet ground state that is predicted for (CO)(2). However, such an orbital crossing does not occur on formation of (CO)(2n+1) from 2n + 1 CO molecules, which is why (CO)(3) and (CO)(5) are both calculated to have singlet ground states. Orbital crossings, involving an antibonding, b(1), combination of lone-pair MOs, occur in forming all (CO)(2n) molecules from 2n CO molecules. Nevertheless, (CO)(6) is predicted to have a singlet ground state, in which the b(2u) σ MO is doubly occupied and the a(2u) π MO is left empty. The main reason for the difference between the ground states of (CO)(4) and (CO)(6) is that interactions between 2p AOs on non-nearest-neighbor carbons, which stabilize the a(2u) π MO in (CO)(4), are much weaker in (CO)(6), due to the much larger distances between non-nearest-neighbor carbons in (CO)(6) than in (CO)(4).     

The nature of the AgI...AgI interaction in different Ag(NH3)2 dimers embedded in supramolecular solids

An isolated silver(I) ammonia monomer, a dimer, and a novel dimer containing an intercalated water molecule have been embedded as guests in supramolecular frameworks, [Ag(NH3)2][(H2thpe)(H3thpe)].MeCN (1), [{Ag(NH3)2}2][(H2thpe)2]4.25 H2O (2), and [{Ag(NH3)2}-H2O-{Ag(NH3)2}][(H2thpe)(2)]benzene (3) (H3THPE=tris(hydroxyphenyl)ethane). The [{Ag(NH3)2}2]2+ dimer is not stable as an isolated entity, but is stabilized by hydrogen bonding in the supramolecular framework. The water-intercalated silver(I) ammonia dimer, which constitutes a novel species, is also subject by hydrogen bonding in concentrated solutions. The destabilization energy of the dimer relative to isolated monomers is calculated to be approximately 300 kJ mol(-1) by both perturbation methods and DFT theory. For the water-intercalated dimer it is calculated to be approximately 200 kJ mol(-1) according to the BSSE-corrected MP2 calculation. The different aggregate states show a dramatic variation of absorption and emission properties, in accordance with the concentration dependent red-shift observed in solutions. Natural-bond-orbital analysis shows that the disilver-ammonium-aquo "sandwich" cation in 3 is stabilized by interaction between the pi lone pair orbital on the oxygen atom of the water molecule and Ag(I)--N sigma antibonding molecular orbital.     

Bicyclo[2.2.1]hepta-2-ene-5-yl-7-ylium radical cation: a theoretical validation of a bishomoaromatic radical cation intermediate

[structure: see text] A natural bond orbital analysis of the distonic bicyclo[2.2.1]hepta-2-ene-5-yl-7-ylium radical cation interprets its structure and radical character by a three-center two-electron bond between C2, C3, and C7 (a bishomoaromatic stabilization) and a singly occupied orbital on C5, n(5). Moreover, B3LYP/6-311+G(d,p) ESR parameters, which agree excellently with experiment, are interpreted in terms of spin polarization in the natural hybrids of sigma(C5-H5), and a dual hyperconjugative effect involving n(5), sigma(C1-H1a), sigma(C1-H1b), and antibonding counterparts.     

Molecular orbital studies of dinitrogen tetroxide and related molecules

Hartree-Fock LCAO MO calculations for N₂O₄ have been performed in a basis of symmetry orbitals formed from a minimal Slater basis set. Effects of rounding and truncation errors were minimized by the use of the symmetry basis, which also allowed the order or tilling of molecular orbitals to be specified independently of orbital energies. Convergence difficulties were overcome by combined use of the conjugate gradients method and Roothaan's iterative procedure; the method of steepest descents was less effective than either of these. Multicentre ‘non-NDDO’ two-electron integrals were evaluated by the gaussian expansion technique. The wavefunction obtained for the lowest state is NN antibonding, largely as a result of the filling of the 6b_1u antibonding sigma orbital in preference to the 6a_g bonding sigma orbital. There is only a small amount of NN pi-bonding. A bond energy analysis shows that the lowest state is markedly stabilized by NNO three-centre interactions.     

Quantum-chemical investigation of nature of neutral intermolecular hydrogen bond in complex H3PO...HF

Results are presented from modeling the complex H₃PO...HF by the ab initio Hartree-Fock-Roothaan method. A generalized method is proposed for the quantitative fragmentary analysis of molecular orbitals (MOs). It is shown that when the complex is formed, the chemical bond between the phosphine oxide and the HF molecule is formed by means of a shift of the electron pair of the -bond of the HF to a 2p orbital of the O atom and the formation of a bonding three-center MO localized on the O, H, and F atoms, and also through a shift of an electron pair from the O atom to a 2p orbital of the F atom and the formation of a nonbonding MO localized on the O and F atoms.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 28, No. 1, pp. 38–41, January–February, 1992.     

Orbital Interaction and the Mulliken-Walsh Diagram for AH2 Systems

We define θ- (or R-) bonding (or antibonding) character of the molecular orbitals according to the slopes of the orbital energy curves when the internuclear angle (or internuclear distance) is varied. So far the slope of the orbital curve has only been accounted for by the qualitative argument based on two factors: the orbital overlap and the s-p mixing. We employ the bond orbitals instead of the usual atomic orbitals as the basis set to analysis the character of the molecular orbitals. The Fock matrix in the bond orbital basis can then quantitatively account for the effects of both the overlap and s-p mixing factors. Our analysis also show that a third factor, the orbital interaction, is essential to account for both the “typical” and “abnormal” behavior of the slopes.     

Structural and spectroscopic characterization of an electrophilic iron nitrido complex

We have isolated and structurally characterized a terminal iron nitrido complex supported by a bulky tris(carbene)borate ligand. The electronic structure of this complex reveals that the a1 LUMO (formerly Fe(dz2)) is strongly stabilized by reduced antibonding interactions with the carbene sigma-donor ligands and configurational mixing (hybridization) with higher lying Fe 4s and 4p atomic orbitals. This unusual bonding interaction results in a low-lying Fe nitrido acceptor orbital (LUMO) that possesses electrophilic character. Reaction with PPh3 results in nitrogen atom transfer to the phosphine, supporting a reaction mechanism involving nucleophilic attack of the triphenylphosphine HOMO at the electrophilic LUMO of the iron nitrido complex.     

Electron delocalization in nickel metallic wires: a DFT investigation of Ni(3)(dpa)(4)Cl(2) and [Ni(3)(dpa)(4)](3+) (dpa = dipyridylamide) and extension to higher nuclearity chains

The electronic structure of Ni(3)(dpa)(4)Cl(2) (1) has been investigated within the framework of the density functional theory (DFT), using two types of exchange-correlation functionals and various basis sets. The "broken-symmetry" approach proposed by Noodleman for the characterization of electronic states displaying an antiferromagnetic coupling has been applied to 1. All calculations lead to the conclusion that the ground state results from an antiferromagnetic coupling between the terminal Ni atoms, both displaying a high-spin electronic configuration. The central Ni atom is in a low-spin configuration, but is involved in a superexchange interaction connecting the two magnetic centers. These results are in agreement with the assignments recently proposed by the group of F. A. Cotton on the basis of magnetic measurements. It is shown that the ground state electronic configuration calculated for 1 provides the trinickel framework with some delocalized sigma bonding character. The observed geometry of 1 is accurately reproduced by the broken-symmetry solution. The doublet ground state assigned to the oxidized species [Ni(3)(dpa)(4)](3+) (2) and the dramatic contraction of the coordination sphere of the terminal metals observed upon oxidation are also confirmed by the calculations. However, the formal Ni-Ni bond order is not expected to increase in the oxidized species. The contraction of the Ni-Ni distance in 2 is shown to result in part from the vanishing of the important trans influence originating in the axial ligands, and for the rest from a more efficient shielding of the metal nuclear charge along the Ni-Ni-Ni axis. The conclusions deduced from the analysis of the bonding in 1 and 2 can be extended to their homologues with higher nuclearity. More specifically, it is predicted that the single occupancy of the most antibonding sigma orbital, extending over the whole metal framework, will provide the (Ni(p))(2)(p)(/(2)(p)(+1)+) chains with some delocalized bonding character and, possibly, with electrical conduction properties.     

Anomeric effect in "high energy" phosphate bonds. Selective destabilization of the scissile bond and modulation of the exothermicity of hydrolysis

A natural bonding orbital (NBO) analysis of phosphate bonding and connection to experimental phosphotransfer potential is presented. Density functional calculations with the 6-311++G(d,p) basis set carried out on 10 model phosphoryl compounds verify that the wide variability of experimental standard free energies of hydrolysis (a phosphotransfer potential benchmark) is correlated with the instability of the scissile O-P bond through computed bond lengths. NBO analysis is used to analyze all delocalization interactions contributing to O-P bond weakening. Phosphoryl bond lengths are found to correlate strongest (R = 0.90) with the magnitude of the ground-state n(O) --> sigma*(O-P) anomeric effect. Electron-withdrawing interactions of the substituent upon the sigma(O-P) bonding orbital also correlate strongly with O-P bond lengths (R = 0.88). However, an analysis of sigma*(O-P) and sigma(O-P) populations show that the increase in sigma*(O-P) density is up to 6.5 times greater than the decrease in sigma(O-P) density. Consequently, the anomeric effect is more important than other delocalization interactions in impacting O-P bond lengths. Factors reducing anomeric power by diminishing either lone pair donor ability (solvent) or antibonding acceptor ability (substituent) are shown to result in shorter O-P bond lengths. The trends shown in this work suggest that the generalized anomeric effect provides a simple explanation for relating the sensitivity of the O-P bond to diverse environmental and substituent factors. The anomeric n(O) --> sigma*(O-P) interaction is also shown to correlate strongly with experimentally determined standard free energies of hydrolysis (R = -0.93). A causal mechanism cannot be inferred from correlation. Equally, a P-value of 1.2 x 10(-4) from an F-test indicates that it is unlikely that the ground-state anomeric effect and standard free energies of hydrolysis are coincidentally related. It is found that as the exothermicity of hydrolysis increases, the energy stabilization of the ground-state anomeric effect increases with selective destabilization of the high-energy O-P bond to be broken in hydrolysis. The anomeric effect therefore partially counteracts a larger resonance stabilization of products that makes hydrolysis exothermic and needs to be considered in achieving improved agreement between calculated and empirical energies of hydrolysis. The avenues relating the thermodynamic behavior of phosphates to underlying structural factors via the anomeric effect are discussed.     

Lewis Acidity Trend of Boron and Aluminium Trihalides: If Not π Back-Bonding,What Else?**

Lewis acidity trend of boron trihalides is a subject that has received a variety of explanations, and still, the simple π back-bonding based one is believed by most, perhaps because of its simplicity, irrespective of opposing findings. Herein we try to give an alternative explanation based on qualitative Molecular Orbital (MO) theory and support that quantitatively by Generalized Kohn-Sham Energy Decomposition Analysis. While the role of orbital overlap on the orbital interaction energy is widely known, the role of electronegativity of the atoms involved is often overlooked. Here we find that the Lewis acidity trend of boron and aluminium halides can be explained by the Wolfsberg-Helmholz (W−H) formula for resonance integral. The MO theory-based predictions are valid only when the orbital interactions are strong enough. In weakly interacting systems, the effect of orbital interactions can be overshadowed by other effects such as Pauli repulsion, dispersion, etc. Thus the Lewis acidity trend of boron and aluminium halides can vary depending on the strength of the interacting Lewis base. We believe that this work would enable one to gain a better understanding not only on the Lewis acidity of boron trihalides and its heavy analogs but also on a variety of related problems such as the stronger π acidity of CS compared to CO and weaker π bonding between heavy atoms.     

On the paucity of molecular actinide complexes with unsupported metal-metal bonds: a comparative investigation of the electronic structure and metal-metal bonding in U2X6 (X = Cl, F, OH, NH2, CH3) complexes and d-block analogues

Density functional calculations have been performed on M2X6 complexes (where M = U, W, and Mo and X = Cl, F, OH, NH2, and CH3) to investigate general aspects of their electronic structures and explore the similarities and differences in metal-metal bonding between f-block and d-block elements. A detailed analysis of the metal-metal interactions has been conducted using molecular orbital theory and energy decomposition methods. Multiple (sigma and pi) bonding is predicted for all species investigated, with predominant f-f and d-d metal orbital character, respectively, for U and W or Mo complexes. The energy decomposition analysis involves contributions from orbital interactions (mixing of occupied and unoccupied orbitals), electrostatic effects (Coulombic attraction and repulsion), and Pauli repulsion (associated with four-electron two-orbital interactions). The general results suggest that the overall metal-metal interaction is stronger in the Mo and W species, relative to the U analogues, as a consequence of a significantly less destabilizing contribution from the combined Pauli and electrostatic ("pre-relaxation") effects. Although the orbital-mixing ("post-relaxation") contribution to the total bonding energy is predicted to have a larger magnitude in the U complexes, this is not sufficiently strong to compensate for the comparatively greater destabilization that originates from the Pauli-plus-electrostatic effects. Of the pre-relaxation terms, the Pauli repulsion is comparable in analogous U and d-block compounds, contrary to the electrostatic term, which is (much) less favorable in the U systems than in the W and Mo systems. This generally weak electrostatic stabilization accounts for the large pre-relaxation destabilization in the U complexes and, ultimately, for the relative weakness of the U-U bonds. The origin of the small electrostatic term in the U compounds is traced primarily to MX(3) fragment overlap effects.     

Synthesis of a one-dimensional metal-dimer assembled system with interdimer interaction, M2(dtp)4 (M = Ni, Pd; dtp = dithiopropionato)

A metal-dimer assembled system, M(2)(dtp)(4) (M = Ni, Pd; dtp = dithiopropionate, C(2)H(5)CS(2-)), was synthesized and analyzed by the X-ray single-crystal diffraction method, UV-vis-near-IR spectra of solutions, solid-state diffuse reflectance spectroscopies, and electrical conductivity measurements. The structures exhibit one-dimensional metal-dimer chains of M(2)(dtp)(4) with moderate interdimer contact. These complexes are semiconducting or insulating, which is consistent with the fully filled d(z)2 band of M(II)(d(8)). Interdimer metal-metal distances were 3.644(2) Angstroms in Ni(2)(dtp)(4) and 3.428(2) Angstroms in Pd(2)(dtp)(4), each of which is marginally longer than twice the van der Waals radius of the metal. Interdimer charge-transfer transitions were nevertheless observed in diffuse reflectance spectra. The origin of this transition is considered to be due to an overlap of two adjacent d(sigma) orbitals, which spread out more than the d(z)2 orbital because of the antibonding d(sigma) character of the M(d(z)2)-M(d(z)2). The Ni(2)(dtp)(4) exhibited an interdimer charge-transfer band at a relatively low energy region, which is derived from the Coulomb repulsion of the 3d(sigma) orbital of Ni.     

Sigma stellation: a design strategy for electron boxes

The carbon-fluorine antibonding (sigma*) orbitals in a fluorocarbon cage are directed toward a central, common point. If the cage is not too large or too small, then the sigma* orbitals will overlap at that point. An added electron can occupy the resulting molecular orbital, suggesting that cage perfluorocarbons will have large electron affinities. This prediction is supported by electronic structure calculations of all of the fluorinated derivatives of tetrahedrane, cyclopropane, and cubane and of some other fluorinated cage and ring compounds. Perfluorododecahedrane (C20F20) is predicted to have an electron affinity of about 3.4 eV, which is equal to that of the fluorine atom. A few speculative extensions and applications are suggested.     

Bonding Energy of a Molecular Orbital(Ⅱ)——Ab initio Calculation

Calculation of the bonding energy of a molecular orbital for a series of small molecules has been carried out by using ab initio STO-3G method. The results obtained demonstrate that the concept of the molecular orbital bonding energy is applicable for judging whether a molecular orbital is bonding, nonbonding or antibonding besides Mulliken overlap criterion.     

The “Inverted Bonds” Revisited: Analysis of “In Silico” Models and of [1.1.1]Propellane by Using Orbital Forces

This article dwells on the nature of “inverted bonds”, which refer to the σ interaction between two sp hybrids by their smaller lobes, and their presence in [1.1.1]propellane. Firstly, we study H₃C−C models of C−C bonds with frozen H-C-C angles reproducing the constraints of various degrees of “inversion”. Secondly, the molecular orbital (MO) properties of [1.1.1]propellane and [1.1.1]bicyclopentane are analyzed with the help of orbital forces as a criterion of bonding/antibonding character and as a basis to evaluate bond energies. Triplet and cationic states of [1.1.1]propellane species are also considered to confirm the bonding/antibonding character of MOs in the parent molecule. These approaches show an essentially non-bonding character of the σ central C−C interaction in propellane. Within the MO theory, this bonding is thus only due to π-type MOs (also called “banana” MOs or “bridge” MOs) and its total energy is evaluated to approximately 50 kcal mol⁻¹. In bicyclopentane, despite a strong σ-type repulsion, a weak bonding (15–20 kcal mol⁻¹) exists between both central C−C bonds, also due to π-type interactions, though no bond is present in the Lewis structure. Overall, the so-called “inverted” bond, as resulting from a σ overlap of the two sp hybrids by their smaller lobes, appears highly questionable.     

Estimating local bonding/antibonding character of canonical molecular orbitals from their energy derivatives. The case of coordinating lone pair orbitals

According to Koopmans theorem, the derivative of the energy of a canonical molecular orbital (MO) with respect to nuclear coordinates quantifies its bonding/antibonding character. This quantity allows predictions of bond length variation on ionisation in a panel of 19 diatomic species. In polyatomic molecules, the derivative of a MO energy with respect to a given bond length reveals the nature and the degree of the bonding/antibonding contribution of this MO with respect to this bond. Accordingly, the HOMO “lone pairs” of CO and CN^? and the HOMO‐2 of CH₃CN are found to be antibonding with respect to the C? X bond (X = N, O), whereas the HOMO of N₂ is found to be bonding. With the same approach, the variation of the bonding character in the MOs of CO and CH₃CN on interaction with an electron acceptor (modeled through the approach of a proton) or by applying an electric field was studied. © 2016 Wiley Periodicals, Inc.     

Novel Colored Systems of the “Inverted Triphenylmethylium Dye” Type Containing Nitrogen,Phosphorus, Sulfur and Congeneric Donor Centers

Abstract

In the course of a fundamental study relating to the question of color and constitution it was found, that a simple HMO-treatment of the isoconjugate resonance system of triphenylmethylium (TPM) dyes¹ provides a very variegated scenery for imagining some novel dye systems. Thus, for the archetype of all TPM-dyes, crystal violet, the spectroscopically relevant frontier orbitals show above a core of nine bonding MO's with a limiting energy of ß, two nonbonding levels (nb), one slightly bonding (b) and one slightly antibonding (ab) MO, respectively. The occupancy of the frontier orbitals is 6, so that the longest wavelength absorption corresponds to an excitation from a nb-MO to the weakly antibonding MO. One sees at once, that diminuation of the frontier orbital occupancy by 4, leaving only 2 electrons, should generate a new dye system presenting approximatly the same color as crystal violet, since now the longest wavelength absorption would correspond to a transition from the (symmetrically situated) slightly bonding MO to a nb-MO.